Is it possible for an inverted energy pyramid to exist explain why or why not?

No i don't think so; this is because in a particular energy pyramid, no additional energy enters the system, and energy is lost to the environment at energy level. An energy pyramid is the pyramid that shows the availability of energy that connects the consumers with the decomposers shows the energy transfer between trophic levels. It shows that less and less food and energy is available as you go from the base to the top of the pyramid.